Answer: The jar contains 40 quarters and 42 nickels.
Step-by-step explanation:
The worth of a quarter is 25 cents. Converting to dollars, it becomes
25/100 = $0.25
The worth of a nickel is 5 cents. Converting to dollars, it becomes
5/100 = $0.05
Let x represent the number of quarters that they have in the jar.
Let y represent the number of nickels that they have in the jar.
Kevin and Randy Muise have a jar containing 82 coins, all of which are either quarters or nickels. This means that
x + y = 82
The total value of the coins in the jar is $12.10. This means that
0.25x + 0.05y = 12.1 - - - - - - - - - - - 1
Substituting x = 82 - y into equation 1, it becomes
0.25(82 - y) + 0.05y = 12.1
20.5 - 0.25y + 0.05y = 12.1
- 0.25y + 0.05y = 12.1 - 20.5
- 0.2y = - 8.4
y = - 8.4/ - 0.2
y = 42
x = 82 - y = 82 - 42
x = 40
Cylinder: 1²(3) = 3
3(9) =27
Prism: 4x3x6 =72
Total: 72+27 = 99in³
Answer:
Answer is 19.2
Step-by-step explanation:
60x60= 3600 63x63= 3969
3969
- 3600 = 369 square root of the 369= is 19.2
Answer:
DA = 285.7 m
Step-by-step explanation:
First we need to find the side AB in the triangle ABC, and we can do this using Pythagoras' theorem:
AB^2 = BC^2 + AC^2
AB^2 = 300^2 + 400^2
AB^2 = 25000
AB = 500 m
We can find the angle ABC with the tangent relation:
tangent(ABC) = 400/300 = 4/3
ABC = 53.13°
From triangle ABC, we have:
ABC + BCA + CAB = 180°
53.13 + 90 + CAB = 180
CAB = 36.87°
From triangle DAC, we have:
DAC + ACD + CDA = 180
36.87 + 45 + CDA = 180
CDA = 98.13°
Now to find the side of DA, we can use law of sines in triangle DAC:
DA/sin(DCA) = AC/sin(CDA)
DA/sin(45) = 400/sin(98.13)
DA = 400 * 0.7071 / 0.9899 = 285.7258 m
Rounding to nearest tenth, we have DA = 285.7 m
